Simplify the following expression: $\dfrac{60x^2}{40x}$ You can assume $x \neq 0$.
Solution: $ \dfrac{60x^2}{40x} = \dfrac{60}{40} \cdot \dfrac{x^2}{x} $ To simplify $\frac{60}{40}$ , find the greatest common factor (GCD) of $60$ and $40$ $60 = 2 \cdot 2 \cdot 3 \cdot 5$ $40 = 2 \cdot 2 \cdot 2 \cdot 5$ $ \mbox{GCD}(60, 40) = 2 \cdot 2 \cdot 5 = 20 $ $ \dfrac{60}{40} \cdot \dfrac{x^2}{x} = \dfrac{20 \cdot 3}{20 \cdot 2} \cdot \dfrac{x^2}{x} $ $\phantom{ \dfrac{60}{40} \cdot \dfrac{2}{1}} = \dfrac{3}{2} \cdot \dfrac{x^2}{x} $ $ \dfrac{x^2}{x} = \dfrac{x \cdot x}{x} = x $ $ \dfrac{3}{2} \cdot x = \dfrac{3x}{2} $